## The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation.(English)Zbl 0860.39034

The main result in the paper is the following. Let $$X$$ be a linear separable $$F$$-space over the set of real (or complex) numbers. If the real (or complex) valued function $$f$$ satisfies $$f(x+f (x)^ny) = f(x)f(y)$$ for all $$x,y \in X$$ then $$f$$ is either continuous or the set of points where $$f(x)$$ is not zero is a Christensen zero set. All continuous solutions are determined.

### MSC:

 39B52 Functional equations for functions with more general domains and/or ranges
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